Chapter 1: Measures of Atmospheric Composition (X1)

1. (i) The mixing ratio of gas X in the atmosphere is constant at 1 ppmv (part per million byvolume). What is the partial pressure PX of X at 100 hPa?(ii) Roughly speaking, how will the number density of X depend on height? Explain.

2. The relative humidity does not change very strongly with height in the troposphere. But thepartial pressure of water vapor in the atmosphere PH2O decreases very rapidly with height. What isthe main reason for this rapid decrease?

3. Draw a general plot of how the partial pressure of water vapor in the atmosphere PH2O dependson height in the troposphere.

Chapter 2: Atmospheric Pressure (X2)

Chapter 3: Simple Models (X3)

1. Measurements indicate that N2O is increasing at a rate of 0.3 % per year. Its current mixing ratiois 315 ppbv. Its mixing ratio in the preindustrial atmosphere was 285 ppbv. It is destroyed (mostlyin the stratosphere) with an overall first order loss rate k = 0.004 (year)−1. Assume that this firstloss rate k is constant. There are 1.8× 1020 moles of air in the atmosphere.(i) Estimate the number of moles of N2O emitted from the surface in the preindustrial atmosphere.(Hint: you can assume that N2O sources and sinks were in balance.)(ii) Estimate the current emission of N2O from the surface (in moles per year).(iii) If the current production were to stay constant, what would be the new steady state N2O mixingratio.(iv) What is the main reason for the increased emission of N2O into the atmosphere?

2. This question involves setting up a two box model of the troposphere and stratosphere. Thetropopause occurs at 150 hPa. The surface is at 1000 hPa. The first order rate constant for thetransfer of mass from the troposphere into the stratosphere is kTS = 0.135 yr−1.NS : number of moles in the stratosphereNT : number of moles in the troposphere(i) Solve for the first order rate constant for the transfer of moles from the stratosphere to thetroposphere (kST ).(ii) The total number of moles in the troposphere and stratosphere is Na = 1.8× 1020. The mixingratio of a CFC is 200 pptv in the troposphere and 150 pptv in the stratosphere. Solve for NCFC,T

and NCFC,S, the number of moles of the CFC in the troposphere and stratosphere respectively.(iii) What is the rate of change of the CFC in the stratosphere (in pptv/year), taking into accounttransport from the troposphere, transport to the troposphere, and chemical loss. The first order lossrate for the chemical loss of the CFC in the stratosphere is kL = −0.1year−1.(iv) If the CFC is increasing in the troposphere at a rate of 25 pptv/year, what is the rate ofemission (in moles/year) of the CFC into the troposphere? Take into account transport to and fromthe stratosphere. Assume that there is no chemical destruction of the CFC in the troposphere.

3. (i) Assume the average pressure at the tropopause is 166 hPa and that the global average surfacepressure is 1000 hPa. Define,MT = mass of the troposphereMS = mass of the stratosphere

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Determine the ratio MS/MT .(ii) Assume a two box model for the atmosphere. If the tropopause pressure does not change withtime, and the transfer rate coefficient kST for transport of air from the stratosphere to the troposphereis 0.7 yr−1, find kTS, the first order rate coefficient for transfer of air from the troposphere to thestratosphere.(iii) The stratosphere contains 90% of the total mass of ozone in the atmosphere. The atmospherecontains 5 ×1013 moles of ozone. Find the number of moles of ozone transported per year fromstratosphere to the troposphere, and from the troposphere to the stratosphere.(iv) The mean concentration of OH in the troposphere is [OH] = 1.2 × 106 molecules/cm3. Thereaction constant for the reaction of OH with methane is 2.6× 10−15cm3/molec− sec. What is thefirst order rate constant kCH4 for the loss of methane via the OH reaction in the troposphere (inunits of yr−1).(v) What is the lifetime of CH4 in the troposphere with respect to transport into the stratosphere(in years)?(vi) What is the lifetime of CH4 in the troposphere with respect to reaction with OH (in years)?(vii) The average mixing ratio of CH4 in the troposphere is 1.7 ppmv (parts per million by volume.)Assume the two losses of CH4 are OH attack and transport to the stratosphere. Assume the onlyCH4 source is surface emission. Assume a mean tropopause pressure of 166 hPa, and that the mixingratio of methane in the atmosphere is constant. Estimate the number of moles of methane emittedfrom the surface per year. (Hint: Find the number of moles in the troposphere.)1 hPa = 100 Pa = 100 N/m2

gravitational acceleration g = 9.80 m/sec2

radius of the earth R = 6400 kmmean molecular weight of air Ma = 28.96 g/mole

4. Gas X is emitted entirely into the Northern Hemisphere. Let mn the mass of X in the NorthernHemisphere and ms the mass of X in the Southern Hemisphere. The first order exchange constantfor the exchange of mass between the two hemispheres is k = 0.9(yr)−1. Gas X has a first order lossrate in the atmosphere of kl = 0.8(yr)−1 in both hemispheres. Calculate mn/ms. (Ignore exchangewith the stratosphere.) You can assume that X is in steady state in both hemispheres.

5. Assume that CFC-12 has an emission rate from the surface of E = 4 × 108 kg/year, and thatthe only removal mechanism from the troposphere is transport to the stratosphere. Assume the firstorder loss rate of CFC-12 in the stratosphere due to photolysis is kL = 0.05 yr−1. Adopt the followingconventions:kST - first order rate constant for the transfer of air from stratosphere to the tropospherekTS - first order rate constant for the transfer of air from troposphere to the stratosphereMCFC,T - mass of CFC-12 in the troposphereMCFC,S - mass of CFC-12 in the stratospherekL - first order chemical loss rate of CFC-12 in the stratosphere(i) Write down an expression for the rate of change of MCFC,T that includes the processes mentionedabove.(ii) Write down an expression for the rate of change of MCFC,S that includes the processes mentionedabove.

Assume:kTS = 0.135 yr−1

kST = 0.77 yr−1

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(iii) Assume that the masses of CFC-12 in the troposphere and stratosphere are at steady state.Evaluate MCFC,S.(iv) What fraction of the total mass of CFC-12 in the atmosphere is in the stratosphere at steadystate?(v) Bonus question: what is the atmospheric lifetime of CFC-12 in the atmosphere (troposphere +stratosphere)?

6. Consider an urban area modeled as a square of size L with a height of h. A gas X is emittedinto the box from the surface at a uniform rate of E (kg/m2sec). X is removed from the box by aconstant wind of strength U. The wind does not result in a flux of X into the box. The density of Xin the box is ρX (kg/m3). Assume that the density of X is uniform in the box. Call the total massof X in the box mx.(i) What is the rate at which X is being emitted into the box (kg/sec)?(ii) What is the rate at which X is being advected out of the box (kg/sec)?(iii) Write down an equation for the rate of change of mX .(iv) What is the density of X (ρX) in the box at steady state?

7. What is dry deposition? Name two atmospheric constituents for which dry deposition can be animportant sink.

Chapter 4: Atmospheric Transport (X4)

What is the residence time of an air parcel in the stratosphere? (About three years) What is thebasic outline of the stratospheric circulation? What is the polar vortex? How does it influence theevolution of the Antarctic ozone hole? How does the ratio of the chemical lifetime of a species tothe dynamical lifetime affect its distribution? The size of the region over which a chemical species isenhanced about a source region is roughly equal to the product of the species lifetime by the ambientwinds.

1. What is the approximate typical residence time of an air parcel in the stratosphere?

2. What is the main reason ozone columns are higher in mid-latitudes than the tropics?

3. Plot the typical seasonal evolution of tropopause height from January to December at a NorthernHemisphere mid-latitude location. Indicate the typical maximum and minimum tropopause heights.Also plot on this figure how you would expect the ozone column to vary over a year.

4. Give an estimate for each timescale.(i) Timescale for vertical overturning in the troposphere.(ii) Timescale for interhemispheric exchange in the troposphere.(iii) Timescale for parcel in the troposphere to go into the stratosphere.(iv) Timescale for parcel in the stratosphere to go into the troposphere.(v) Timescale for parcel to be dispersed in east-west direction.(vi) Timescale for mixing within a hemisphere.

5. How does total ozone column respond to changes in tropopause height. Explain.

Chapter 5: The Continuity Equation (X5)

Chapter 6: Geochemical Cycles (X6)

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1. The preindustrial atmosphere contained sulfur compounds emitted by marine phytoplankton andvolcanoes, and NOx emitted by soils and lightning. These sources accounted globally to 1 × 1012

moles S/year and 1× 1012 moles N/year, respectively. Assume that all the emitted sulfur and NOx

are oxidized in the atmosphere to H2SO4 and HNO3 respectively, which are then scavenged by rain.Radius of the earth =(i) Estimate the mean concentrations (M) of SO4

2− and NO3− in rain, assuming a global mean

precipitation rate over the earth of 2 mm/day.(ii) Assuming there was nothing else present to influence the acidity of rainfall, estimate the meanpH of rain in the preindustrial atmosphere.(iii) In reality there was an additional important natural source of acidity to the background atmo-sphere. Specify what it was, and indicate the reactions by which it increased [H+].(iv) There were also natural sources of alkalinity to the preindustrial atmosphere. Specify one andindicate the reactions by which it would have decreased [H+].

2. (i) When CO2 dissolves in the ocean, it can assume one of the following three chemical forms:CO2 · H2O, HCO3

−, or CO32−. Make a plot of the relative contribution of each of these three forms

to the total CO2(aq) as a function of ocean pH. Indicate on this diagram the current pH of the ocean,and therefore, the dominant form of CO2(aq).(ii) Fossil fuel emissions of CO2 are increasing the concentration of dissolved CO2 in the ocean. Isthis expected to increase or decrease ocean pH? Explain using relevant chemical reactions.(iii) This change in pH has an important impact on the ability of the ocean to uptake additionaldissolved CO2. Explain.

3. The CO2 and O2 cycles are strongly coupled.(i) Discuss one process which couples the two cycles on long (geological) time scales.(ii) Discuss one process which couples the two cycles on short (seasonal) time scales.(iii) Which process is more likely to exert greater control on the mean level of O2 in the atmosphere.Explain.

4. What is a mechanism by which CO2 in the ocean mixed layer is removed to the deep ocean.

5. What is one pathway by which N2 in the atmosphere can enter the biosphere?

6. What are two natural sources of NOx to the atmosphere?

7. We discussed in class why biomass does not exert a strong controlling influence on O2 levels inthe atmosphere. Over long timescales, what are the main sources and sinks of oxygen to and fromthe atmosphere?

8. (i) Atmospheric Oxygen O2 shows a small seasonal variation. At what time of year wouldyou expect oxygen concentrations to be a maximum. Explain. (Assume you are in the NorthernHemisphere).(ii) Estimate the size of this seasonal variation (i.e. ∆O2/O2 where ∆O2 is the change in mixingratio from minimum to maximum, and O2 is the average value). The mean mixing ratio of O2 in theatmosphere is 0.2. The seasonal variation in CO2 is about 5 ppmv. Respiration and photosynthesiscan be described by:

nCO2 + nH2O ↔ (CH2O)n + nO2

(iii) The oxygen concentration of the atmosphere currently has a negative trend. Why?

9. Nitrogen fixing bacteria play a special role in the nitrogen cycle. What do they do? (i.e. how dothey interconvert nitrogen?)

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10. (i) Do increasing atmospheric CO2 concentrations increase or decrease the pH of the oceans?Explain using the relevant reactions.(ii) Suppose some process were to decrease the pH of the oceans (i.e. increase the [H+] concentration.)Would this tend to drive CO2 from the atmosphere into the ocean or from the ocean into theatmosphere? Explain using the relevant chemical equations.

11. What are two mechanisms by which O2 is removed from the atmosphere?

12. What is a mechanism by which N2 is removed from the atmosphere?

13. What is a mechanism by which CO2 is removed from the surface mixed layer of the ocean?

14. Are increasing atmospheric CO2 concentrations expected to increase or decrease the pH of theoceans? Explain with reference to the relevant reactions.

16. What are two ways in which carbon near the surface is transported to the deep ocean?

17. The CO2 and O2 cycles are strongly coupled.(i) Discuss one process which couples the two cycles on long (geological) time scales.(ii) Discuss one process which couples the two cycles on short (seasonal) time scales.(iii) Which process is more likely to greater control on the mean level of O2 in the atmosphere.Explain.

18. The oceans can, in principle, take up most of the CO2 emitted into the atmosphere by fossil fuelburning. There are a variety of factors which inhibit ocean uptake of CO2. Discuss one.

19. What are two gases emitted in volcanic plumes?

20. Define net primary productivity (NPP).

21. Does growth of corals (Ca2+ + CO32− → CaCO3(s)) cause atmospheric CO2 to increase or

decrease? Explain briefly.

22. What is a geological sink of O2 from the atmosphere?

Chapter 7: The Greenhouse Effect (X7)

Chapter 8: Aerosols (X8)

1. What is a source of sulfate aerosols to the stratosphere?

Chapter 9: Chemical Kinetics (X9)

Estimating oxygen column above a certain pressure: The pressure at an altitude z, p(z), is equal tothe weight of the atmospheric column above that height per unit area. You have to go from pressureto mass per area, from mass per area to moles per area, then use the oxygen mixing ratio to getmoles oxygen per unit area, then multiply by Avogadros number to get molecules O2 per unit area(molecule column amount). For oxygen you can always assume a constant mixing ratio of 0.2. Theozone mixing ratio is always height dependent.

p(z) =Weight of air column above z

area of column

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Define M(z) as the mass of the air column above z per unit area. g is the gravitational acceleration:p(z) = M(z)g. Define NO2(z) as the number of O2 molecules above a height per unit area. If M(z)has units of kg

m2 , then

NO2(z) = M(z)× 1000 g

kg× 1mole air

28.964 g× 6.02× 1023molec air

1 mole air× 0.21molecO2

1 molec air× m2

104 cm2

This will give you NO2(z) in molecules O2 per cm2. If nO2(z) is the oxygen concentration as a functionof height, then

NO2(z) =∫ ∞z

nO2(z)dz.

1. Assume that 1 percent of the incident top of the atmosphere solar flux at 300 nm reaches theground. Also assume that the only significant absorber in the atmosphere at this wavelength is ozone,and that scattering can be neglected. The ozone absorption cross section at 300 nm is 34.3× 10−20

cm2 per molecule. The solar zenith angle is 60 o (from the vertical).

(i) What is the optical depth δ of the atmosphere at a solar zenith angle of 60 o from the vertical?The transmissivity T is transmitted flux divided by the incident. Here you are given T = 0.01. UseT = e−δ/cosθ. Solve for the optical depth given T and θ.(ii) What is the optical depth δ of the atmosphere for overhead sun?Same as (i) except θ = 0.(iii) What is the column ozone amount in molecules per cm2?The optical depth δ equals column amount times the molecular cross section. Make sure units con-sistent.(iv) What is the ozone column in Dobson Units? 1 Dobson Unit = 2.69× 1016 molecules per cm2.Just a unit conversion.

2. Species X has an absorption cross section of σ = 1 × 10−20 cm2 per molecule at a particularwavelength. Assume that at this wavelength, it is the only species which absorbs or scatters radiation.When the sun is at an angle of 30 degrees from the vertical (θ = 30o ), 10 % of the solar radiationincident at the top of the atmosphere is absorbed before it reaches the ground. What is the columnconcentration of species X? (By column concentration N is meant the vertically integrated numberof molecules per unit area above a particular point.)

4. The photolysis rates of NO2 and NO3 are almost independent of height. Explain.

5. Figure 2.5 in “Research Problems in Atmospheric Chemistry” can be primarily understood on thebasis of absorption by oxygen and ozone. The oxygen absorption cross sections are given in Figure3.3 and ozone cross-sections are given in Figures 3.4 and 3.5. Assume the atmosphere is isothermalat 280 K, oxygen is 21 percent of the atmosphere, and the ozone layer is 300 Dobson Unit thick atthe ground, 200 Dobson at 20 km, and 50 Dobson at 30 km. 1 DU = 2.69× 1020 molecules per m2.Assume a solar zenith angle of 60o , as has been done in the figure.(i) Calculate the optical depth and fractional transmissions at 200 nm from ozone and oxygen at 20and 30 km.(ii) Which gas is more important?(iii) Is it consistent with the figure?(iv) Do the same at 250 and 300 nm.(v) What is the reason for the “window” region at about 220 nm?

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7. Show a plot of how the photolysis rate of a species like N2O, which is destroyed by UV light,typically depends on height from the surface to 50 km.

8. (i) Suppose the transmissivity of the atmosphere at a particular wavelength due to an absorberis is 0.01. What is the optical depth at that wavelength?(ii) Suppose the concentration of the absorber in the atmosphere were doubled. What would be thenew transmissivity?

9. Suppose the optical depth of the atmosphere at a particular wavelength is 3. what fraction of thesun’s radiation at that wavelength would you expect to reach the surface?

12. The intensity of UV radiation at the surface, under clear sky conditions, is dependent on whattwo main variables. (ozone column and solar zenith angle).

13. Assume that 1 percent of the incident top of the atmosphere solar flux at 300 nm reaches theground. Also assume that the only significant absorber in the atmosphere at this wavelength is ozone,and that scattering can be neglected. The ozone absorption cross section at 300 nm is 34.3× 10−20

cm2 per molecule. The solar zenith angle is 60 o (from the vertical). 1 Dobson Unit = 2.69 × 1016

molecules per cm2. What is the ozone column in Dobson Units?

15. Species X has a constant mixing ratio of 100 ppbv in the atmosphere, i.e. Cx = 1.0× 10−9. Theabsorption cross-section of X at 300 nm is 1.0× 10−16 cm2/molecule.Assume:Pressure at the surface = P0 = 1.0× 105 N/m2.gravitational acceleration = g = 9.80 m/sec2

Mean molecular weight of air = Ma = 28.96 g/moleAvogadros number = Na = 6.02 × 1023 molec/mole(i) What is the total atmospheric column of X (in molec/cm2)?(ii) What is the optical depth of X in the atmosphere at 300 nm?(iii) If there are no other absorbers in the atmosphere at 300 nm, what fraction of the incoming solarradiation at 300 nm reaches the surface?

16. Suppose molecule A is dissociated by light with wavelengths less than 250 nm, while moleculeB is dissociated by visible light. Roughly plot how the photolysis rates of A and B would depend onaltitude.

17. The O3 absorption cross-section at 300 nm is 34.3 ×10−20 cm2. The O3 column is 8 × 1018

molec/cm2. Assume the sun is directly overhead (ie. solar zenith angle of zero).(i) What is the optical depth of the atmosphere due to O3 at 300 nm?(ii) What is the percentage increase in 300 nm flux at the surface if the O3 column decreases by 5 %?

18. Assume molecule A is photolyzed by visible light. Plot how you would expect its photolysis rateto depend on height in clear sky conditions. Assume molecule B is photolyzed by far UV light ofabout 200 nm. Plot how you would expect its photolysis rate to depend on height (roughly).

19. Species X is photolyzed mainly by photons with wavelengths of 280-300 nm. Species Y isphotolyzed mainly by photons in the range 550-600 nm.(i) Contrast how you would expect the photolysis rates of species X and Y to depend on height bydrawing a schematic diagram.(ii) Contrast how you would expect the photolysis rates of species X and Y to depend on solar zenithangle by drawing a schematic diagram.

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(iii) What is a dominant physical process determining the actinic flux at the surface in the 280-300nm range.(iv) What is an important physical process determining the actinic flux at the surface in the 550-600nm range. could say: aerosols, clouds, solar zenith angle, altitude, ozone from Cappuis ozone band.

21. (i) What is the main atmospheric absorber of radiation between 100 and 242 nm?(ii) What is the main atmospheric absorber of radiation between 242 and 350 nm?

22. (i) Give the expression by which photolysis rates (J values) are calculated. Identify all variables.(ii) The J values of species with very fast photolysis rates (such as eg. NO2 and NO3) usually havevery little height, or solar zenith angle, dependence. Explain.

23. Suppose at some wavelength the atmosphere has an optical depth of 2. What fraction of incidenttop of the atmosphere solar flux at this wavelength reaches the surface?

24. The absorption cross-section of species A and B are shown below.(i) How would you expect the photolysis rate of species A to depend on height? Why?(ii) How would you expect the photolysis rate of species B to depend on height? Why?

Chapter 10: Stratospheric Ozone (X10)

Stratospheric Ozone: Chapman ozone chemistry (S1)

1. The scheme for ozone production and destruction involving Ox species only is called the Chapmanscheme.(i) How is Ox produced in this scheme? What is the Ox production rate?

(ii) How is Ox destroyed in this scheme? Write out two Ox destroying cycles and specify the Ox

destruction rate in terms of the relevant reactant concentrations and reactions constants.

(iii) What is a successful prediction of this scheme?

(iv) What is a failure of this scheme?

2. Ozone concentrations are largest near 30 km. Why do ozone concentrations decrease with heightabove 30 km, and decrease toward the surface?

3. Give two reasons why the concentration of atomic oxygen [O] increases rapidly with height in thestratosphere.

4. Give two reasons for the rapid increase in the O/O3 ratio with height in the stratosphere.

5. (i) Why does Ox production go to zero at high altitudes?(ii) Why does Ox production become small as you approach the surface?

6. Specify how many Ox are created (+) or destroyed (-) in the following reactions.(i) O +O → O2

(ii) O1D +N2 → O +N2

(iii) O2 + hν → O +O(iv) O1D +H2O → 2OH

7. At an altitude of approximately 40 km, the temperature is 260 K, and the pressure is 3 hPa.Assume the set of reactions:

O2 + hν → O +O JO2 = 2× 10−10sec−1

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O3 + hν → O +O2 JO3 = 6× 10−4sec−1

O +O2 +M → O3 +M k1 = 8.3× 10−34cm6molec−2sec−1

O +O3 → 2O2 k2 = 3.0× 10−15cm3molec−1sec−1

The rate constant given for the reaction between O and O2 is the low temperature limit.A form of the ideal gas law is that the density of air (molec/m3) is given by

na =AvP

RT

where Av is Avogadro’s number (6.023 × 1023 molec/mole), P is pressure in Pa, R is the ideal gasconstant (8.31Jmol−1K−1) and T is temperature.[O2] ≈ 0.2 [M], where [M] is the total density (ie. [M] = na)(i) Given this reaction scheme, determine the O/O3 ratio. You may use family style approximations.(ie. instantaneous production and loss of a member of a family is dominated by reactions whichinterconvert family members). You may also make appropriate steady state assumptions.Asking you to derive the O/O3 ratio given in the lecture notes.(ii) Find the O3 concentration. (Hint: impose steady state in Ox)Asking you to derive the O3 expression given in the lecture notes.(iii) Convert the O3 concentration to a mixing ratio in parts per billion (ppbv)Use the expression given for na (i.e. the ideal gas law) to convert a concentration to a mixing ratio.

8. Indicate how many Ox are destroyed or produced by the following reactions.O2 + hν → O +OO3 + hν → O1D +O2

O3 +O → 2O2

O2 +O → O3

9. (i) Derive the Chapman expression for the ozone concentration. You may make all necessaryfamily style approximations. Write [O2] = CO2 [M], where [M] is the total number density of theatmosphere (sometimes called na). Your final answer should express [O3] in terms of JO2 , JO3 , k1,k2, CO2 , and [M]. Assume the following reactions:JO2 : O2 + hv → O + Ok1 : O + O2 + M → O3 + MJO3 : O3 + hv → O2 + Ok2 : O + O3 + M → 2 O2

Given in the lecture notes. Note that photolysis rates here labeled as J values but indicated by k’s inthe text.(ii) Make a plot of the typical vertical variation of JO2 as a function of height from the surface to 50km.Oxygen photolysis shown in the lecture notes and text. Photolysis rate near zero below 20 km since noflux with wavelength below 240 nm reaches these levels, due to overhead oxygen and ozone absorption.Photolysis rate converges to a constant value at high altitudes since so little overhead atmosphere andvery little attenuation of top of the atmosphere solar flux.(iii) Make a plot of the typical vertical variation of [O3] as a function of height from the surface to50 km as predicted by the Chapman expression. Explain the behavior at high and low altitudes.

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Given in the lecture notes. As discussed in the notes, the ozone concentration from this expressiongoes to zero in the troposphere (or below 20 km) since oxygen photolysis zero. Goes to zero above 30km, since [M] goes to zero.(iv) What is the main failure of the Chapman expression for [O3]? Explain the reasons for thisfailure.Discussed in the lecture notes: ozone too big since expression does not include all sinks.

10. (i) What are the sources and sinks of Ox in Chapman (oxygen only) chemistry.(ii) Derive the Chapman expression for the ozone concentration using family style approximations.

11. What is the main reason O3 concentrations decrease above 35 km?

12. What is the main failing of Chapman ozone chemistry (ie. Ox species only) when compared toobserved ozone concentrations?

13. Why is there a stratospheric ozone layer? I.e. why does the production of ozone become smallhigh up in the atmosphere, and why does it become smaller in the troposphere?

15. Using odd-oxygen chemistry alone, and suitable family style approximations, calculate the O/O3

and O1D/O3 ratios at 20 and 40 km. Compare your answers with what you can estimate from page199 of the JPL handouts.

16. Show that the O2 photolysis source of O is indeed much smaller than the two O3 photolysissources at 20 and 40 km. That is, that rates of recycling between Ox family members are much largerthan the rate of input into the family.

Stratospheric Ozone: Catalytic ozone destruction by HOx, NOx, ClOx (S2)

1. (i) Assume that an air parcel in the stratosphere consists of the following gases only: O2, O3, O,O1D, H2O, N2, OH, and HO2. Draw a diagram showing the above species and the reactions betweenthem. Use the list of all possible reactions on the accompanying pages. Ignore the photolysis of H2O,but include the two photolysis channels of O3, and the photolysis of O2. Do not include reactioninvolving species not in the above list.(ii) What is the source of ozone?(iii) What are the sinks of ozone?(iv) What is the source of HOx?(v) What is the sink of HOx?(vi) Derive an implicit expression for [O3] in terms of the J values, rate constants, and the concen-trations of O2, N2, and H2O. Do not try to solve this expression.

2. (i) Write out a chemical cycle involving NOy and HOx species which destroys HOx. Point out theexistence of competing reactions at some of the steps.

(ii) Write out a chemical cycle involving NOy and HOx species, and the N2O5 aerosol reaction, inwhich HOx is created. Again, some of the steps will not always occur because of the existence ofcompeting reactions. Point these out.

3. Specify two ways in which the presence of NOy species slows down ozone destruction from ClO.

4. Give two ways in which the presence of NOx (= NO + NO2) slows down rates of ozone destructiondue to other catalytic cycles (either HOx or ClOx). In your discussion specify the relevant reactions.

6. (i) Write down a complete sequence of reactions by which members of the NOy family destroyHOx. By complete sequence is meant a cycle in which each NOy species involved gets produced anddestroyed.

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(ii) Write down a complete sequence of reactions by which members of the NOy family can produceHOx.

7. Consider the following reactions only:

OH +O3 → HO2 +O2 k14 = 2.0× 10−14 cm3/molec− secHO2 +O3 → OH + 2O2 k15 = 1.0× 10−15 cm3/molec− secOH +HO2 → H2O +O2 k17 = 1.5× 10−10 cm3/molec− sec[M ] = 2× 1018molec/cm3.OH = 0.6 pptvO3 = 4 ppmv(i) HOx destroys Ox in the stratosphere via a catalytic cycle. What is the sequence of reactions inthis cycle?(ii) Estimate the length of time it takes a HOx molecule to destroy one Ox.(iii) Estimate the number of Ox molecules destroyed by one HOx before it itself is destroyed. (ie. theHOx chain length).

8. How does the presence of NOx (NO or NO2) inhibit Ox destruction by HOx? Specify relevantreaction(s).

9. How does the presence of HOx (OH or HO2) inhibit Ox destruction by NOx? Specify relevantreaction(s).

11. How does Ox destruction by ClOx depend on NOx? Give a reason for this dependence. Specifya reaction if possible.

12. (i) Write down a sequence of reactions involving HOx or NOx species which results in catalyticozone (Ox) destruction.(ii) How would you express the rate of Ox destruction by this cycle?

13. Write out two catalytic cycles which destroy Ox in the stratosphere.

14. In the stratosphere, Ox is destroyed by catalytic cycles involving HOx, NOx, and ClOx radicals.For each family below, indicate if the N2O5 aerosol reaction increases or decreases Ox destruction bythat family, and give a reason why.(i) HOx

(ii) NOx

(iii) ClOx

15. Show that the net rate of Ox destruction by HOx can be written:d[Ox]/dt = -2k2[HO2][O3],where one assumes that HOx interacts with Ox through the following reactions:k1: OH + O3 → HO2 + O2

k2: HO2 + O3 → OH + 2 O2

k3: HO2 + NO → NO2 + OHHint: By far the dominant sink of NO2 is: NO2 + hv → NO + O.

16. Define the Ox family. Why is the lifetime of Ox much longer than the lifetimes of its individualmembers? Specify which of the following reactions destroy, produce, or conserve Ox.O +O2 +M → O3 +MO +NO2 → O2 +NOO + ClO → O2 + Cl

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O3 + hν → O2 +OO +O → O2

O +OH → O2 +HO1D + CH4 → OH + CH3

17. Studies have shown that NOx injected into the stratosphere from high speed aircraft will probablydecrease the rate of ozone destruction by ClOx. Why? Specify a relevant reaction in your answer.

18. The rate of ozone destruction due to NOx (NO + NO2) is usually defined as -2k[O][NO2], wherek is the reaction constant for the O + NO2 reaction. This is based on the assumption that NO willalways react with O3 to make NO2. This is incorrect.(i) What is the next most important NO to NO2 conversion pathway? (Do this by looking in JPL 94for things that give up an oxygen atom to NO, and calculate the NO lifetime for this reaction basedon the JPL concentrations.)(ii) What is the probability that they will occur relative to the likelihood of NO reacting with ozone?Use concentrations and temperatures at 20 km of JPL ’94.(iii) If these alternative pathways are taken, will ozone still be destroyed ordinarily? Are you in dangerof “double counting”? ie., counting one net ozone destruction twice from two different cycles?

Stratospheric Ozone: HOx Partitioning (S3)

2. Consider the following reactions only:

1.O1D +H2O → 2OH k1 = 2.2× 10−10 cm3/molec− sec

2.OH +HO2 → H2O +O2 k2 = 4.8× 10−11e250/T cm3/molec− sec

3.HO2 +NO → OH +NO2 k3 = 3.7× 10−12e240/T cm3/molec− sec

4.HO2 +O3 → OH + 2O2 k4 = 1.1× 10−11e−500/T cm3/molec− sec

5.OH +O3 → HO2 +O2 k5 = 1.6× 10−12e−940/T cm3/molec− sec

(i) The pressure is 50 hPa, the temperature is 220 K, O3 = 3 ppmv, H2O = 5 ppmv, NO = 100pptv, and [O1D] = 3 molec/cm3. Using appropriate “family-style” approximations, solve for theconcentration of OH. (If I asked this equation again I would break it into parts, and give you thevalues of the reaction constants. The OH/HO2 ratio can be solved from using reactions 3, 4, 5 only.Then impose steady state on HOx. Reaction 1 produces HOx, and reaction 2 destroys HOx.)(ii) What is the lifetime of water with respect to attack by O1D?

4. What is a reaction which destroys HOx in the stratosphere?

5. (i) Derive a steady state expression for the concentration of H2O2 in terms of the concentrationsof [OH], [HO2], JH2O2 , and relevant reaction rates.

(ii) Use this expression and the JPL concentration profiles to predict the H2O2 concentration at 20km and compare your answer with the JPL modeled concentration at 20 km.

7. (i) Derive a steady state expression for the concentration of H2O2 in terms of the concentrationsof [OH], [HO2], JH2O2 , and relevant reaction rates.(ii) Use this expression and the JPL concentration profiles to predict the H2O2 concentration at 20km and compare your answer with the JPL modeled concentration at 20 km.

8. (i) Define f as the fraction of O1D atoms that react with water vapor to make two OH hydroxylradicals rather than than being quenched back to O. Calculate this at the ground with a temperature

12

of 300 K and 100 percent humidity, and at 30 km with a temperature consistent with the JPL profileand 5 ppmv (parts per million) of water vapor.

(ii) What is the Ox lifetime associated with O1D + H2O at the two heights? For 30 km, assumethe JO3→O1D value in JPL, and for the ground, extrapolate from 10 km.

Stratospheric Ozone: NOx Partitioning (S4)

9. Assume the following reactions:NO +O3 → NO2 +O2 k1 = 2.0× 10−14 cm3/molec− secNO2 +OH +M → HNO3 +M k2 = 7.0× 10−12 cm3/molec− secNO2 + hν → NO +O JNO2 = 0.01 sec−1

HNO3 + hν → NO2 +OH JHNO3 = 7.0× 10−7 sec−1

The pressure ([M]) dependence has been included in k2.The mixing ratio of O3 is 2 ppmv.The mixing ratio of OH is 1.0 pptv.Assume that NOx (= NO + NO2) can be treated as a family.[M ] = 2× 1018molec/cm3.(i) Evaluate the [NO]/[NO2] ratio. You may use family style and steady state approximations.(ii) Evaluate the [NOx]/[HNO3] ratio. You may use family style and steady state approximations.

10. Assume the following set of reactions:

NO +O3 → NO2 +O2

NO2 +O → NO +O2

NO2 + hν → NO +O JNO2 = 0.01 sec−1

O3 + hν → O +O2 JO3 = 0.0005 sec−1

O +O2 +M → O3 +M

The mixing ratio of O3 is 5 ppmv.[M ] = 2× 1018molec/cm3.The mixing ratio of NOx ( = NO + NO2) is 500 pptv.The temperature is 220 K.Using family style and steady state approximations,(i) What is the concentration of atomic oxygen?(ii) What is the NO/NO2 ratio?(iii) What is the lifetime of NO2 with respect to photolysis?(iv) What is the lifetime of NO2 with respect to reaction with O?(v) The rate of Ox destruction from NOx is often written −2k[NO2][O]. Explain.(vi) What is the lifetime of Ox with respect to destruction by NOx?

11. For simplicity, let [NOy] = [NO] + [NO2] + [HNO3].[NOx] = [NO] + [NO2]

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[M ] = 2× 1018molec/cm3.OH = 0.6 pptvO3 = 4 ppmv

Consider the following reactions only:

NO2 + hν → NO +O JNO2 = 0.01 sec−1

HNO3 + hν → NO2 +OH JHNO3 = 7.0× 10−7 sec−1

NO2 +OH +M → HNO3 k34 = 7.0× 10−12 cm3/molec− secHNO3 +OH → H2O +NO2 +O k32 = 4.0× 10−13 cm3/molec− secNO +O3 → NO2 +O2 k1 = 3.0× 10−15 cm3/molec− sec(i) Estimate the [NO]/[NO2] ratio using family style approximations for NOx.(ii) Assuming that NOx is in steady state, and using the [NO]/NO2] ratio given above, solve for the[NOx]/[HNO3] ratio.(iii) What is the lifetime of NOx with respect to conversion to HNO3?

12. Assume the following reactions:NO +O3 → NO2 +O2 k1 = 2.0× 10−14 cm3/molec− secNO2 +OH +M → HNO3 +M k2 = 7.0× 10−12 cm3/molec− secNO2 + hν → NO +O JNO2 = 0.01 sec−1

HNO3 + hν → NO2 +OH JHNO3 = 7.0× 10−7 sec−1

The pressure ([M]) dependence has been included in k2 (i.e. leave out [M] when writing out thisreaction rate.)The mixing ratio of O3 is 2 ppmv.The mixing ratio of OH is 1.0 pptv.Assume that NOx (= NO + NO2) can be treated as a family.Total molecular density: [M ] = 2× 1018molec/cm3.(i) Evaluate the [NO]/[NO2] ratio. You may use family style and steady state approximations.(ii) Evaluate the [NOx]/[HNO3] ratio. You may use family style and steady state approximations.

Stratospheric Ozone: ClOx Partitioning (S5)

16. Consider the following reactions.HCl +OH → Cl +H2O k1 = 2.6× 10−12e−350/T cm3/molec− secCl + CH4 → HCl + CH3 k2 = 1.1× 10−11e−1400/T cm3/molec− secCl +O3 → ClO +O2 k3 = 2.9× 10−11e−260/T cm3/molec− secClO +NO → Cl +NO2 k4 = 6.4× 10−12e290/T cm3/molec− sec

Assume:Temperature = 220 KPressure = 50 hPaO3 = 2 ppmvCH4 = 1.6 ppmvOH = 1 pptvNO = 500 pptv

(i) Use local steady state assumptions to derive an expression for the ClHCl

ratio.(ii) Treat ClOx ( = Cl + ClO) as a subfamily of Cly, and use local steady state, to derive andexpression for the Cl

ClOratio.

(iii) Use these expressions and the above species concentrations to calculate the ClOHCl

ratio.

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17. This question involves estimating the increase in ClO associated with a decrease in NOx, asmight occur for example from a volcanic eruption. This is a hard question. If gave in the futurewould break up into smaller parts.Assume:

NOx decreases from 400 pptv to 200 pptv.The effect of ClO on NOx partitioning is negligible.Consider the species Cl, ClO, ClONO2, HCl, NO, NO2, CH4, OH, and O3 only.All species can be assumed to in steady state, or specified as given below.[Cly] = [ClO] + [Cl] + [ClONO2] + [HCl]Total Cly is 2 ppbv.NOx (= NO + NO2) and ClOx (= Cl + ClO) can be treated as families.[OH] = 1 pptv (independent of NOx)[O3] = 2 ppbv[CH4] = 1.0 ppmvTemperature = 195 K, Pressure = 50 hPa, [M] = 1.8× 1018 molec/cm3.

Assume the following reaction set:

(R1) Cl +O3 → ClO +O2 k1 = 7.6× 10−12 cm3/molec− sec(R2) Cl + CH4 → HCl + CH3 k2 = 8.4× 10−15 cm3/molec− sec(R3) ClO +NO2 +M → ClONO2 +M k3 = 1.2× 10−12 cm3/molec− sec(R4) ClO +NO → Cl +NO2 k4 = 2.8× 10−11 cm3/molec− sec(R5) NO +O3 → NO2 +O2 k5 = 1.5× 10−15 cm3/molec− sec(R6) NO2 + hν → NO +O JNO2 = 0.01 sec−1

(R7) OH +HCl→ Cl +H2O k7 = 4.3× 10−13 cm3/molec− sec(R8) ClONO2 + hν → ClO +NO2 JClONO2 = 5.0× 10−5sec−1

(i) Derive an expression for the ClO/ClONO2 ratio.(ii) Derive an expression for the Cl/HCl ratio.(iii) Derive an expression for the Cl/ClO ratio.(iv) Evaluate the mixing ratio of ClO when NOx = 400 pptv.(v) Evaluate the mixing ratio of ClO when NOx = 200 pptv.

18. Define Cly = Cl + ClO + HCl. The total Cly is 2 ppbv. Assume the following reactions:Cl + CH4 → HCl + CH3 k1 = 1.9× 10−14 cm3/molec− secClO +NO → Cl +NO2 k2 = 2.3× 10−11 cm3/molec− secCl +O3 → ClO +O2 k3 = 8.9× 10−12 cm3/molec− secHCl +OH → Cl +H2O k4 = 5.3× 10−13 cm3/molec− secYou may treat ClOx (= Cl + ClO) as a family.You can assume that HCl is in steady state with ClOx.NO : 100 pptvO3 : 2 ppmvCH4 : 1.2 ppmvOH : 1 pptv(i) Evaluate the Cl/ClO ratio.(ii) Evaluate the Cl/HCl ratio.(iii) Evaluate the ClO mixing ratio (in pptv)

Stratospheric Ozone: NOy, N2O, and Denitrification (S6)

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3. It has been reasonably well established from aircraft measurements that denitrification occurs inboth the Arctic and Antarctic. What measurements have been used to establish this? Summarizethe arguments based on these measurements used to support denitrification. A schematic plot mayhelp.

4. As an air parcel is transported within the Brewer-Dobson circulation, would you expect themixing ratio of NOy ( = NO + NO2 + HNO3 + NO3 + N2O5 + ClONO2) to increase or decreasewith time? What is the main reason for this? (Increases with time due to O1D attack on N2O).

5. During the Antarctic winter, it is believed that nitric acid trihydrate particles (NAT or typeI PSC’s) serve as nucleation sites for type II PSC’s consisting of ice. Type II PSC’s are largeenough to fall significant distances during their lifetime. The resulting depletion of NOy within theAntarctic polar vortex is called denitrification. It is thought that this enhances ozone depletion byslowing down the conversion of active chlorine (Cl + ClO + Cl2O2 etc.) to reservoir chlorine (HCl+ ClONO2). How would it do this?

6. (i) What is denitrification?(ii) How does it enhance polar ozone depletion?(iii) Ozone depletion does not occur inside the polar night. Why?(iv) In the absence of denitrification NOy mixing ratios will be typically higher inside the vortex thanoutside. Why?

8. The only sink of NOy in the stratosphere (other than the fallout of nitrogen containing polarstratospheric cloud crystals over the winter poles) is the N + NO → N2 + O reaction. Calculate thelifetime of NOy associated with this reaction at 30 km using the JPL 1994 profiles.

9. Figure 19.8 shows simultaneous measurements of NOy and N2O taken at about 20 km from theER-2. The decrease in N2O is at 76o N, and the increase in NOy at the same latitude, are associatedwith a crossing of the polar vortex. (This would be an interesting assignment question but would notbe given on a quiz.)(i) Make a scatter plot of NOy versus N2O (ie. NOy against N2O.)(ii) Use the plot to estimate the fraction of N2O molecules that undergo reaction with O1D to produce2 NO.

Stratospheric Ozone: Aerosol Chemistry (S7)

11. Studies have shown that the injection of NOx into the stratosphere from a projected fleet of highflying aircraft will decrease chlorine catalyzed ozone destruction. Explain.

12. The effect on ozone levels of a volcanic eruption which increases aerosol surface areas in thestratosphere depends on the chemical composition of the stratosphere. Explain.

13. It is currently accepted that the increases in aerosol surface area in the stratosphere associatedwith explosive volcanic eruptions reduce total column ozone. But one hundred years ago, it is likelythat these reductions were smaller, or that a volcanic eruption may have actually increased totalcolumn ozone. Give an argument as to why the response of the ozone layer to volcanic eruptions islikely to have changed in this way.

15. For each of the following radical families, indicate whether the N2O5 aerosol reaction increasesor decreases ozone destruction by that family. Also give a reason for this change, being as specificas possible with a particular reaction(s) in your explanation.(i) NOx

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(ii) HOx

(i) ClOx

20. It has been recognized that extremely large volcanic eruptions such as the eruption of Mt.Pinatubo will not reduce NOx/NOy ratios to zero in the stratosphere even though they dramaticallyincrease sulphate aerosol surface areas. At some point, NOx/NOy ratios become insensitive to in-creases in aerosol surface area. This is referred to as saturation. Aerosol mediated NOx to HNO3

conversion occurs at night when NO2 is converted to NO3, then N2O5, and the N2O5 then reactswith water on the aerosol. When there is lots of aerosol surface area, virtually every N2O5 created atnight gets converted to HNO3 rather than being photolyzed to NOx the next morning. In this case,the rate limiting step in converting NOx to HNO3 via the aerosol pathway becomes the formationof NO3. An estimate of the upper limit effect of the the N2O5 aerosol reaction can be obtained byassuming that every NO3 formation reaction at night effectively destroys two NOx. This question istoo hard to ask in a quiz(i) Why two NOx?

(ii) Calculate the diurnally averaged (24 hour averaged) NOx lifetime associated with the aerosolloss. Assume a 12 hour night and the temperature, ozone concentration, and number densities at 20km in JPL ’97. (Hint: the NO2 concentration at night = the NOx concentration.)

(iii) Make an estimate of the diurnally averaged NOx lifetime associated with the NO2 + OH reaction.As a rule of thumb, it is fairly accurate to say that the diurnally averaged concentration of a radicallike OH is about one-third the noon value, given a 12 hour day. Also you will need for this questionto express the noon NO2 concentration in terms of NOx, using the usual steady state approximations.You can assume that NOx is constant over the day.

(iii) What is the net lifetime of NOx with respect to both loss processes. (Hint: you add lifetimes asreciprocals. Eg. the net loss lifetime from two processes is

1

τnet=

1

τ1+

1

τ2.

(iv) What is the diurnally averaged nitric acid photolysis rate (the J value) at 20 km? Again dividenoon value by three to get the diurnally averaged rate.

(v) Estimate the NOx/NOy ratio with and without the N2O5 aerosol reaction. Assume that thecontributions of NO3, N2O5, and ClONO2 to NOy are small enough to be ignored. There are acouple of different ways of doing this. One is to start from as assumption of NOx steady state,using the approximations for the NOx and HNO3 loss rates given above, or proceed directly fromthe relative lifetimes.

Stratospheric Ozone: Polar Stratospheric Clouds (S8)

21. (i) Suppose that reactions on polar stratospheric clouds (PSC’s) have converted most of thereservoir chlorine species (HCl and ClONO2) to active chlorine ClOx, where ClOx is defined as thesum of ClO and 2.*Cl2O2. If the mixing ratio of ClOx is 2 ppbv, estimate the mixing ratio of ClO.Assume that the partitioning of ClOx can be calculated assuming photochemical equilibrium, thatthe reactions which determine this partitioning are given below, and that the photolysis of Cl2O2 iseffectively the source of two ClO since ClOO rapidly decomposes to Cl and Cl reacts rapidly withozone to make ClO. The pressure is 60 hPa (about 20 km) and the temperature is 195 K.

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ClO + ClO +M → Cl2O2 +M k1 = 1.83× 10−13(cm3sec)−1

Cl2O2 + hν → Cl + ClOO JCl2O2 = 4.0× 10−3sec−1

The density [M] can be calculated from temperature T and pressure P (in hPa) using

[M ] =P

T · 1.38× 10−19.

(ii) The rate of ozone destruction by the cycle involving the chlorine dimer Cl2O2 is 2k1[ClO][ClO].What is the lifetime of ozone with respect to this cycle if the ozone mixing ratio is 3 ppmv?(iii) Calculate the lifetime of ozone with respect to the ClO + O catalytic cycle. Assume that O andO1D form a very small fraction of Ox, and that the Ox family can be partitioned using photochemicalequilibrium assumptions.

O3 + hν → O +O2 JO3 = 5.0× 10−4

O +O2 +M → O3 +M k2 = 3.5× 10−15

ClO +O → Cl +O2 k3 = 4.3× 10−11

23. (i) Write down two reactions that occur on the surfaces of polar stratospheric clouds (PSC’s).(ii) What is their effect on nitrogen and chlorine partitioning?(iii) Why do they increase ozone destruction?

24. Write down a reaction that occurs on polar stratospheric clouds and explain why it leads toenhanced ozone destruction.

25. Consider the following reactions involving Cl, ClO, Cl2O2, HCl, ClONO2, O3, O, NO, and NO2.(Note: the products of Cl2O2 photolysis are taken to be Cl + Cl + O2; ie. the ClOO produced byCl2O2 photolysis is assumed to immediately thermally dissociate into Cl and O2.) (On a quiz, thisquestion would be broken into smaller parts to be more easilly solvable.)Cl +O3 → ClO +O2 k1 = 7.6× 10−12 cm3/molec− secClO +O → Cl +O2 k2 = 4.3× 10−11 cm3/molec− secClO +NO → Cl +NO2 k3 = 2.8× 10−11 cm3/molec− secClO + ClO +M → Cl2O2 +M k4 = 1.6× 10−13 cm3/molec− secClO +NO2 +M → ClONO2 +M k5 = 1.2× 10−12 cm3/molec− secO +O2 +M → O3 +M k6 = 3.0× 10−15 cm3/molec− secCl + CH4 → HCl + CH3 k7 = 8.4× 10−15 cm3/molec− secNO +O3 → NO2 +O2 k8 = ×10− cm3/molec− secO3 + hν → O +O2 JO3 = 6.0× 10−4sec−1

NO2 + hν → NO +O JNO2 = 1.0× 10−2sec−1

Cl2O2 + hν → 2Cl +O2 JCl2O2 = 1.0× 10−3sec−1

Also assume:Temperature = 195 KPressure = 50 hPa[M ] = P×7.25×1018

Tmolec/cm3, P in hPa and T in K

O3 = 2 ppmvCH4 = 1.6 ppmv

18

NO = 50 pptvClO = 1500 pptv

Note: the [M] dependence of the three body rate constants has already been absorbed into the rateconstant.(i) Write down two catalytic cycles involving ClO which destroy ozone.(ii) Calculate the rate of ozone destruction from each of the two cycles. Convert your answers toppbv per day. You may use family style approximations to partition Ox.(iii) What is the lifetime of O3 with respect to each of the two cycles?(iv) Calculate the Cl2O2 mixing ratio (in pptv). You may assume that Cl2O2 is in steady state.(v) Calculate the mixing ratio of Cl (in pptv). You may assume that ClOx ( = Cl + ClO + Cl2O2)can be treated as a family and partitioned in the usual way.(vi) Calculate the lifetime of ClOx with respect to conversion to HCl.(vii) Calculate the lifetime of ClOx with respect to conversion to ClONO2. You may also use familystyle approximations to partition NOx (= NO + NO2).

26. After an air parcel has been exposed to a PSC, how does the presence of NOx in the air parcelincrease the rate at which ClOx is converted back to both ClONO2 and HCl? Be as specific aspossible in referring to the particular reactions, or reaction sequences, by which this occurs.

27. Number the following events as they would occur in sequence over the South Pole during a polarozone depletion event. (i.e. 1 - 6 with 1 the first event that occurs.)Cl2 photolyzes

NOx increases

PSC’s start to form

Polar vortex temperatures become colder

Ozone and ClOx become anticorrelated

HCl mixing ratios decrease

28. A plane flying in the stratosphere is equipped to measure ClO, O3, and NO. These measurementsgive:

[NO] = 20 pptv (parts per trillion)[O3] = 6 ppmv (parts per million)[ClO] = 2000 pptv (parts per trillion)

Assume the following reactions:

O +O2 +M → O3 +M k1 = 1.7× 10−15 cm3molec−1sec−1

ClO +O → Cl +O2 k2 = 4.3× 10−11 cm3molec−1sec−1

ClO + ClO +M → Cl2O2 +M k3 = 6.4× 10−13 cm3molec−1sec−1

ClO +NO → Cl +NO2 k4 = 2.8× 10−11 cm3molec−1sec−1

Cl +O3 → ClO +O2 k5 = 7.6× 10−12 cm3/molec− secCl2O2 + hν → 2Cl +O2 JCl2O2 = 1.0× 10−3 sec−1

O3 + hν → O +O2 JO3 = 6× 10−4 sec−1

The temperature is T = 195 K.

The total number density of the air is [M] = 2× 1018 molec/cm3.

You may treat the pressure dependent reaction rates as if the [M] dependence is included in the k’s.

Use all family partitioning and steady state approximations you think appropriate.

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[ClOx] = [Cl] + [ClO] + [Cl2O2][Ox] = [O] + [O3]

[O2] = 0.2 [M]

(i) Calculate the [O]/[O3] ratio.(ii) Calculate the lifetime of Ox with respect to destruction by the ClO + O catalytic cycle.(iii) Calculate the mixing ratio of Cl2O2.(iv) Calculate the lifetime of Ox with respect to destruction by the ClO + ClO reaction catalyticcycle.(v) Estimate the Cl/ClO ratio.

29. What is wrong with this sentence: ”The annual springtime 50 % reduction in total ozone columnover the Antarctic has always occurred because polar stratospheric clouds have always existed at thistime in the Antarctic.”

30. Provided there is sufficient total reactive chlorine Cly, what are the two main preconditions forrapid polar ozone destruction?

31. The ClO mixing ratio of an air parcel is measured to be 2 ppbv.The temperature is T = 195 K.The mixing ratio of O3 is 6 ppmv.The total number density of the air is [M] = 2× 1018 molec/cm3.[O2] = 0.2 [M]Consider the following reactions only:

O3 + hν → O +O2 JO3 = 6× 10−4sec−1

O +O2 +M → O3 +M k1 = 8.3× 10−34cm6molec−2sec−1

ClO +O → Cl +O2 k2 = 4.3× 10−11cm3/molec · 1/secClO + ClO +M → Cl2O2 +M k3 = 3.2× 10−31cm6/molec2 · 1/secUsing appropriate family style and steady state approximations:

(i) What is the lifetime of Ox with respect to destruction the O + ClO cycle?(ii) What is the lifetime of Ox with respect to destruction the ClO + ClO dimer cycle?(iii) Roughly plot how the rates of ozone destruction from the two Ox destroying cycles given abovewould depend on the ClO concentration.

34. We have discussed in class three catalytic cycles involving chlorine which destroy ozone. Inthe reaction labeling given below, one of these is reaction 1 followed by reaction 2, and another isreaction 3, followed by reactions 4 and 1. Until we started discussing ozone depletion chemistry, weignored the second cycle. This question involves justifying that the dimer cycle can be ignored inthe background case. Let [ClO] = 50 pptv in the background case, and [ClO] = 2000 pptv in an airmass perturbed by PSC’s. In answering this question, make any approximations you think can bejustified, eg. family partitioning etc. Unless otherwise specified, all species can be assumed to be insteady state. Consider the reactions listed below only.[ClOx] = Cl + ClO + 2 Cl2O2

[O3] = 2 ppmv[NO] = 100 pptvTemperature = 195 K, Pressure = 50 hPa, [M] = 1.8× 1018 molec/cm3.(R1) Cl +O3 → ClO +O2 k1 = 7.6× 10−12 cm3/molec− sec(R2) ClO +O → Cl +O2 k2 = 4.3× 10−11 cm3/molec− sec(R3) ClO + ClO +M → Cl2O2 +M k3 = 1.6× 10−13 cm3/molec− sec(R4) Cl2O2 + hν → 2Cl +O2 JCl2O2 = 1.0× 10−3sec−1

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(R5) O3 + hν → O +O2 JO3 = 6.0× 10−4sec−1

(R6) ClO +NO → Cl +NO2 k6 = 2.8× 10−11 cm3/molec− sec(R7) O +O2 +M → O3 +M k7 = 3.0× 10−15 cm3/molec− sec(i) Calculate the mixing ratio (in pptv) of Cl2O2 in the background case.(ii) Calculate the mixing ratio (in pptv) of Cl2O2 in the PSC perturbed case.(iii) Calculate the mixing ratio (in pptv) of O.(iv) What percent of the chlorine ozone destruction in the background case is due to the dimercycle?(v) What percent of the total ozone destruction in the PSC perturbed case is due to the dimer cycle?

35. What is the main reason polar ozone depletion is more extensive over the South Pole than theNorth Pole?

41. A plane flying in the stratosphere is equipped to measure ClO, O3, and NO. These measurementsgive the following mixing ratios:

CNO = 20 pptv (parts per trillion)CO3 = 6 ppmv (parts per million)CClO = 2000 pptv (parts per trillion)

Assume the following reactions:

O +O2 +M → O3 +M k1 = 1.7× 10−15 cm3molec−1sec−1

ClO +O → Cl +O2 k2 = 4.3× 10−11 cm3molec−1sec−1

ClO + ClO +M → Cl2O2 +M k3 = 6.4× 10−13 cm3molec−1sec−1

ClO +NO → Cl +NO2 k4 = 2.8× 10−11 cm3molec−1sec−1

Cl +O3 → ClO +O2 k5 = 7.6× 10−12 cm3/molec− secCl2O2 + hν → 2Cl +O2 JCl2O2 = 1.0× 10−3 sec−1

O3 + hν → O +O2 JO3 = 6× 10−4 sec−1

The temperature is T = 195 K.

The total number density of the air is [M] = 2× 1018 molec/cm3.

You may treat the pressure dependent reaction rates as if the [M] dependence is included in the k’s.

Use all family partitioning and steady state approximations you think appropriate.

[ClOx] = [Cl] + [ClO] + [Cl2O2][Ox] = [O] + [O3] [O2] = 0.2 [M]

(i) Calculate the [O]/[O3] ratio.(ii) Calculate the lifetime of Ox with respect to destruction by the ClO + O catalytic cycle.(iii) Calculate the mixing ratio of Cl2O2.(iv) Calculate the lifetime of Ox with respect to destruction by the ClO + ClO reaction catalyticcycle.(v) Estimate the Cl/ClO ratio.

Stratospheric Ozone: Ozone variability (S9)

44. Ozone column amounts tend to be higher in mid-latitude and polar regions than in the tropicseven though ozone production rates are higher in the tropics. Explain

21

45. In which regions of the stratosphere is the concentration of ozone least likely to be in instanta-neous photochemical equilibrium with its sources and sinks? Where is equilibrium most likely to bevalid?

46. Ozone columns and UV exposure fluctuate from day to day in response to weather systemswhich change the height of the tropopause. Why?

47. Plot how the total ozone column depends on season (from January through December) at atypical mid-latitude location.

48. Stratospheric ozone production rates are largest in the tropics but ozone column amounts arehigher in mid-latitudes. Why?

49. Plot the typical variation of ozone column amounts (Dobson units) over a year at a NorthernHemisphere mid-latitude location. What is the main reason for this variation?

50. Plot how the ozone column varies over the course of a year at a mid-latitude location. What isthe mean reason for this variation?

51. (i) Plot how tropopause height typically depends on season at a typical mid-latitude location ingoing from January to December.(ii) Plot how ozone column typically depends on season at a typical mid-latitude location in goingfrom January to December.(iii) On a clear day, what are the two main variables that affect the level of UV radiation at thesurface?(iv) What time of year would you typically expect UV levels at the surface to maximized at a typicalmid-latitude location? Be as specific as possible. (2 point)

Stratospheric Ozone: CFC’s and other long-lived tracers (S10)

52. An air parcel enters the stratosphere from the troposphere with particular mixing ratios of CH4

(methane), N2O, NOy, CFC-11, and water. Which of these gases will see their mixing ratios increase,which will decrease, and which will be unchanged?

53. (i) What is the main natural ”source gas” of Cly to the stratosphere? (0.5 point)(ii) What is the main natural ”source gas” of HOx to the stratosphere? (0.5 point)(iii) What is the main natural ”source gas” of NOy to the stratosphere? (0.5 point)

54. Most of the CFC’s released into the atmosphere are ultimately destroyed (and release theirchlorine atoms) in the tropical stratosphere, where levels of UV light are high. It is sometimesclaimed that if CFC’s were destroying ozone, we would therefore be more likely to observe ozonedestruction in the tropics, and not in the polar regions as actually happens. Why is this reasoningincorrect?

55. Why are the CFC’s chemically stable in the troposphere but not in the stratosphere?

56. Suppose the water vapor concentration in the stratosphere were to double. Discuss two ways howthis might lead to increased ozone destruction in the stratosphere. (More HOx and more PSC’s.)

For the most part, the only way to get analytic approximations for relationships between speciesconcentrations is to use family style approximations in conjunction with local steady state assump-tions. Try to be familiar with this approach and how it can be applied in different situations. Themost difficult thing to understand about it is why it is possible to ignore a reaction in one case but

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not another. For example, why can I ignore O2 photolysis when calculating the O/O3 ratio, but notwhen calculating the Ox concentration?

Chapter 11: Oxidizing Power of the Troposphere (X11)

Oxidizing Power of the Troposphere: HOx Production (T1)

1. Why is the hydroxyl radical sometimes referred to as the “detergent” of the atmosphere. Givetwo factors which affect its concentration.

2. What are the two main variables which drive the seasonal variation of OH concentrations in thetroposphere?

3. (i) Where in the troposphere is the concentration of OH typically largest?(ii) Give two reasons for this.

4. The input of NOx and CO into the troposphere is many times larger now than it was one hundredyears ago. The oxidation of each of these species (to HNO3 and CO2 respectively) results in the lossof one OH. But the concentration of OH has probably remained stable, or in some areas increased,over the past one hundred years. What is the main reason why OH has not gone down as much asyou might expect?

5. (i) How is HOx produced?(ii) What are two factors that affect the production of HOx?

6. Assume the following conditions in the upper troposphere: (This question would be simplified ifgiven on a quiz.).T = 220 KPressure = 200 hPaPH2O = 0.05 hPa[M] = 6.6× 1018 molec/cm3

CNO = 50 pptvCCO = 80 ppbv[O3] = 40 ppbvAssume the following reaction set:

(R1) HO2 +NO → OH +NO2 k1 = 1.1× 10−11 cm3/molec− sec(R2) OH +O3 → HO2 +O2 k2 = 2.2× 10−14 cm3/molec− sec(R3) HO2 +O3 → OH + 2O2 k3 = 1.1× 10−15 cm3/molec− sec(R4) O1D +H2O → 2OH k4 = 2.2× 10−10 cm3/molec− sec(R5) O1D +N2 → O +N2 k5 = 3.0× 10−11 cm3/molec− sec(R6) O3 + hν → O1D +O2 JO3 = 2.0× 10−5sec−1

(R7) OH + CO(+O2)→ HO2 + CO2 k7 = 1.7× 10−13cm3/molec− sec(R8) HO2 +HO2 → H2O2 +O2 k8 = 4.6× 10−12 cm3/molec− sec(R9) OH +NO2 → HNO3 k9 = 1.2× 10−11 cm3/molec− sec(R10) NO2 + light→ NO +O k10 = 1.2× 10−2 sec−1

(R11) NO +O3 → NO2 +O2 k11 = 3.4× 10−15 cm3/molec− secAssume HOx, NOx, and [O1D] are in steady state, and that HOx and NOx can be partitioned usingfamily style approximations.(i) Solve for [OH]/[HO2].

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(ii) Solve for [NO]/[NO2]. (Assume HO2 small.)(iii) Solve for [O1D] (molec/cm3).(iv) Calculate the ozone production efficiency of NO.(v) Solve for the HO2 mixing ratio (in pptv). (Hint: The solution involves solving a quadraticequation. Explain how you would solve if you don’t have time for the answer. Ax2 + Bx + C = 0

and x =−B±√

(B2−4AC)

2A

(i) Answer To solve for OH/HO2, restrict attention to HOx partitioning reactions: 2,7,3,1.POH = LOHk3[JO2][O3] + k1[HO2][NO] = k2[OH][O3] + k7[OH][CO]Re-arranging gives:[OH]/[HO2] = (k3[O3]+k1[NO])/(k2[O3]+k7[CO])[O3] = CO3[M], etc.Since [M] is on the top and bottom for all species,[OH]/[HO2] = (k3*CO3+k1*CNO)/(k2*CO3+k7*CCO)CO3 = 40E-09, CNO = 50E-12, CCO = 80E-09You should know what ppmv, ppbv, pptv are etc. It also very important to know that it is

concentration (not mixing ratios) that enter the equation, though as in the case above, [M] cancancel.

[OH]/[HO2] = 0.041

(ii) Answer NOx is a family, so only relevant reactions are k1,k10,k11, but since you don’t know[HO2] I said you could ignore (in reality it is usually small compared to NO+O3).

k10[NO2] = k11[NO][O3][NO]/[NO2] = k10/(k11[O3]) = 13.4

(iii) AnswerJO3[O3] = k5[O1D][N2] + k4[O1D][H2O]Since [M] would be on both sides, can write:JO3*CO3 = k5[O1D]*CN2 + k4[O1D]*CH2O[O1D] = JO3*CO3/(k5*CN2 + k4*CH2O)CN2 = 0.8CH2O = 0.05/200CO3 = 40E-09This gives [O1D] = 0.03 molec/cm3

(iv) Answere = PO3/LNOx = k1[NO][HO2]/k9[NO2][OH]Using the ratios [NO]/[NO2] and [HO2]/[OH] above, get e = 300

(v) Answer Set LHOx = PHOxk8[HO2][HO2] + k9[OH][NO2] = 2*k4[O1D][H2O]Computationally, it saves time to replace all concentrations with mixing ratios. Can do this since

there is an [M][M] in each term.k8*CHO2*CHO2 + k9*COH*CNO2 = 2*k4*CO1D*CH2OAbove found [O1D], so know CO1D = [O1D]/[M].Also know CH2O.Use R = [OH]/[HO2] from above, and given CNO2.CHO2**2 + (k9/k8)*R*CHO2*CNO2 - 2*k4/k8)*CO1D*CH2O = 0This is a quadratic equation in CHO2, with A = 1.

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Should get CHO2 = 16 pptv.

7. There has been some speculation on how ozone depletion in the stratosphere might affect theoxidizing capacity of the troposphere. Discuss two mechanisms of how this might occur.

8. Ozone columns have decreased over the past several decades. How might this have affectedconcentrations of OH in the troposphere? Specify a relevant reaction if possible.

9. (i) Plot the typical dependence of the OH concentration on NO in the troposphere.(ii) What is the main reason for the dependence of OH on NO at low NO?(iii) What is the main reason for the dependence of OH on NO at high NO?(iv) Give three species for which OH attack is the main oxidation mechanism.(v) How is OH thought to have changed over North America since preindustrial times?(vi) What is the main reason for this change?(vii) Is this change mainly good or bad? Explain.

10. (i) Is the concentration of OH in remote regions of the Southern Hemisphere likely to haveincreased or decreased since preindustrial times. Explain.(ii) Is the average concentration of OH near the surface over land in the Northern Hemisphere likelyto have increased or decreased since preindustrial times. Explain.

11. (i) Define f as the fraction of O1D atoms that react with water vapor to make two OH hydroxylradicals rather than than being quenched back to O. Calculate this at the ground with a temperatureof 300 K and 100 percent humidity (water vapor pressure equals 35 hPa), and at 30 km with atemperature consistent with the JPL profile and 5 ppmv (parts per million) of water vapor.(ii) What is the Ox lifetime associated with O1D + H2O at the two heights? For 30 km, assume theJO3→O1D value in JPL, and for the ground, extrapolate from 10 km.

12. A much higher percentage of the O1D that is produced from O3 photolysis is used to helpproduce OH near the surface than in the stratosphere. What is the main reason for this?

Oxidizing Power of the Troposphere: HOx Partitioning (T2)

1. Shown below is a plot of model calculated HO2 and OH concentrations at two latitudes versusthe NO mixing ratio. Assume that CO and O3 are kept constant while NO is varied. Assume thatthe reactions that determine the HOx partitioning in the model are

OH + CO → H + CO2 k1 = 2.4× 10−13

H +O2 +M → HO2 +M k2 = 1.7× 10−12

OH +O3 → HO2 +O2 k3 = 6.8× 10−14

NO +HO2 → NO2 +OH k4 = 8.3× 10−12

HO2 +O3 → OH + 2O2 k5 = 2.1× 10−15

[M ] = 2.1× 1019 molec

cm3

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ozone mixing ratio = 60 ppb.

The pressure dependence of the second reaction has already been included in the rate constant.(i) Calculate the lifetime of HO2 with respect to NO and O3 at 15 o N when the NO mixing ratio is1 pptv.(ii) Estimate the CO mixing ratio using the HO2

OHratio at NO = 1 pptv and 15 o N.

2. (i) In the troposphere, OH concentrations typically increases with NO when the NO concentrationis very low. What is the main reason for this?(ii) How does this increase help explain the hemispheric asymmetry in OH concentrations?(iii) What is the main reason HOx concentrations decrease at large NO?

4. (i) What is the dominant sink of HOx in the troposphere at low NOx?(ii) What is the dominant sink of HOx in the troposphere at high NOx?

5. What are the four main reactions which interconvert OH and HO2 in the troposphere. (Two fromOH to HO2, and two from HO2 to OH).(ii) There are four different pathways using the above four reactions to go from OH to HO2, thenback to OH. Indicate these four cycles, and indicate which of them produces O3, which destroys O3,and which is neutral to O3.(iii) Which cycle would you expect to be dominate in a polluted area (i.e. near fossil fuel emissions).(iv) Which cycle would you expect to be dominate in a pristine area (i.e. far from fossil fuel emis-sions).

7. (i) At low NOx, emissions of NO into the atmosphere from pollution tends to increase OH. Explainusing the relevant reactions.(ii) At high NOx, emissions of NO into the atmosphere from pollution tends to decrease OH. Explainusing the relevant reactions.

8. Assume the following conditions: (If giving this again use HO2 + HO2 reaction as the dominantHOx sink. Give formula for dependence of PSat on temp. Clarify M in OH + NO2.)

Pressure = 1000 hPaTemperature = 298 KO3 = 50 ppbvCO = 80 ppbvRelative humidity = 80 %.JO3→O1D+O2

= 1 × 10−5 sec−1

JNO2 = 0.01 sec−1

Assume the O1D concentration can be calculated by assuming steady state between production fromozone photolysis, quenching by O2 and N2, and reaction with water vapor.

Assume the HO2/OH ratio can be calculated according to steady state with HO2 reacting with O3

and NO, and OH reacting with O3 and CO only.

Assume HOx can be considered a family with O1D + H2O → the only HOx source and OH + HO2

→ H2O + O2 and OH + NO2 → HNO3 the only HOx sinks.

Assume that there is steady state relationship between NO and NO2 formed by NO2 photolysis andthe reaction of NO with O3.

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In your plots assume a range of NO concentrations from 1 pptv to 10 ppbv. Use a logarithmic scalefor NO.

(i) What is the water vapor concentration?

(ii) What is the concentration of O1D?

(iii) Derive an analytical expression for the dependence of HO2/OH on NO.

(iv) Plot the HO2/OH ratio versus NO.

(v) Derive an expression for NO2 in terms of O3, and JNO2 and NO.

(vi) Using steady state for HOx, and HOx family style approximations, solve for the concentrationof OH and HO2 versus NO.

(vii) Plot the concentrations of OH and HO2 versus NO. Use pptv for your units of OH and HO2.

(viii) It is really only valid to consider HOx a family when the dominant sink of OH is conversion toHO2. For what range of NO concentrations is this valid?

Oxidizing Power of the Troposphere: Ox Production (T3)

1. Why are ozone concentrations lower in the troposphere than the stratosphere? Give at least tworeasons.

2. The reaction CH3O2 + NO is considered an ozone production reaction. Explain.

3. What are two reactions which are considered to destroy ozone in the troposphere?

4. O3 concentrations tend to be low in the remote marine boundary layer. Give three reasons.

5. Consider the following reactions involving OH, HO2, H2O2, O3, NO, NO2, H2O, CO, H, O2, O1D,N2, and O2. (Excessively complicated question that would not be directly asked on a quiz.)

NO +O3 → NO2 +O2 k1 = 2.0× 10−12e−1400./T cm3/molec− secNO2 +OH +M → HNO3 k2 = 2.6× 10−30[M ](300

T)3.2 cm3/molec− sec

HO2 +HO2 → H2O2 +O2 k3 = 2.3× 10−13e600/T cm3/molec− secOH + CO → H + CO2 k4 = 1.5× 10−13(1 + 0.6× pmb/1013)

HO2 +NO → OH +NO2 k5 = 3.7× 10−12e250/T cm3/molec− secH +O2 +M → HO2 +M k6 = 5.7× 10−32[M ](300

T)1.6 cm3/molec− sec

O1D +H2O → 2OH k7 = 2.2× 10−10 cm3/molec− secO1D +N2 → O +N2 k8 = 1.8× 10−11e110/T cm3/molec− secO1D +O2 → O +O2 k9 = 3.2× 10−11e70/T cm3/molec− secOH +O3 → HO2 +O2 k10 = 1.6× 10−12e−940/T cm3/molec− secHO2 +O3 → OH + 2O2 k11 = 1.1× 10−14e−500/T cm3/molec− secHO2 +OH → H2O +O2 k12 = 4.8× 10−11e250/T cm3/molec− secNO2 + hν → NO +O JNO2 = 1.0× 10−2sec−1

O3 + hν → O1D +O2 JO3 = 2.0× 10−5sec−1

Also assume:Temperature = 300 KPressure = 1013 hPaO3 = 50 ppbv

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CO = 80 ppbv[H2O] = 0.01 [M] (ie. one part per hundred water vapor)NO = 100 pptv(i) Derive an expression for the HO2/OH ratio from the above reactions, and evaluate it for theconditions listed. You can use family style approximations to partition HOx (= H + OH + HO2).(ii) Calculate the OH and HO2 mixing ratios (in pptv). You can assume the formation of HNO3 andH2O2 are pure HOx sinks (eg. are removed by rainout or surface deposition so don’t photolyze toregenerate HOx). You can also use family style approximations to partition NOx (= NO + NO2).(iii) What are the four main terms in dO3/dt in the above system of reactions.(iv) Evaluate each of these four terms.(v) What is the net rate of ozone production in ppbv/day?

6. At what time of year do Northern Hemisphere ozone concentrations at the surface typically peak.Give two reasons.

7. In the troposphere, net ozone production rates tend to be more positive in the upper tropospherethan near the surface. Give a reason for this.

8. NOx concentrations in remote regions of the equatorial Pacific are usually very small. In thisproblem, we assume that all NOy species concentrations are zero. The concentrations of O3, O, O1D,H2O, OH, HO2, H, O2, N2, CO, and CO2 are nonzero. Do not consider reaction rates or photolysisrates other than those listed below.

Pressure = 950 hPaTemperature = 295 KH2O = 10000 ppmvO3 = 20 ppbvCO = 70 ppbv[N2] = 0.79 [M ][O2] = 0.20 [M ]

Photolysis RatesO3 + hν → O +O2 JO3 = 6.0× 10−4sec−1

O3 + hν → O1D +O2 JO3 = 2.0× 10−5sec−1

Reaction RatesO +O2 +M → O3 +M k1 = 2.9× 10−15

O1D +N2 → O +N2 k8 = 1.8× 10−11e110/T cm3/molec− secO1D +O2 → O +O2 k9 = 3.2× 10−11e70/T cm3/molec− secO1D +H2O → 2OH k7 = 2.2× 10−10 cm3/molec− secHO2 +O3 → OH + 2O2 k2 = 1.07× 10−15

OH +O3 → HO2 +O2 k4 = 2.0× 10−14

OH + CO → H + CO2 k4 = 1.5× 10−13(1 + 0.6× pmb/1013)

H +O2 +M → HO2 +M k6 = 5.7× 10−32[M ](300T

)1.6 cm3/molec− secHO2 +OH → H2O +O2 k12 = 4.8× 10−11e250/T cm3/molec− sec(i) What fraction of O1D atoms react with H2O?(ii) What is the concentration of O1D? Assume that the sources and sinks of O1D are in steadystate.(iii) Use family style approximations to calculate the HO2/OH ratio.(iv) Use family style approximations to calculate the concentrations of OH and HO2.(v) Calculate the net rate of change of the ozone mixing ratio, in ppbv/day.

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(vi) What is the lifetime of ozone?

9. This question is designed to show that net ozone production in the upper troposphere is generallypositive, but that it is usually negative near the surface in the absence of elevated NOx.Surface case: T = 300 K, pressure = 1000 hPa, PH2O = 20 hPa, [M] = 2.4× 1019 molec/cm3.Upper tropospheric case: T = 220 K, pressure = 200 hPa, PH2O = 0.05 hPa, [M] = 6.6 × 1018

molec/cm3.[NO] = 50 pptv in both cases.[CO] = 80 ppbv in both cases.[O3] = 40 ppbv in both cases.It can be assumed that HOx is in steady state with its sources and sinks, and can be partitionedusing family style approximations.It can be assumed that [O1D] is in steady state.

Assume the following reaction set:

(R1) HO2 +NO → OH +NO2 k1 = 3.7× 10−12e250/T cm3/molec− sec(R2) OH +O3 → HO2 +O2 k2 = 1.6× 10−12e−940/T cm3/molec− sec(R3) HO2 +O3 → OH + 2O2 k3 = 1.1× 10−14e−500/T cm3/molec− sec(R4) O1D +H2O → 2OH k4 = 2.2× 10−10 cm3/molec− sec(R5) O1D +N2 → O +N2 k5 = 1.8× 10−11e110/T cm3/molec− sec(R6) O3 + hν → O1D +O2 JO3 = 2.0× 10−5sec−1

(R7) OH + CO(+O2)→ HO2 + CO2 k7 = 1.5× 10−13(1 + 0.6× pmb/1013)(R8) HO2 +HO2 → H2O2 +O2 k8 = 2.3× 10−13e600/T cm3/molec− sec(i) Solve for the [OH]/[HO2] ratio at the surface.(ii) Solve for the [OH]/[HO2] ratio in the upper troposphere.(iii) Solve for [O1D] at the surface.(iv) Solve for [O1D] in the upper troposphere.(v) In this reaction scheme, what reaction is the source of HOx?(vi) In this reaction scheme, what reaction is the sink of HOx?(vii) Solve for [HO2] at the surface.(viii) Solve for [HO2] in the upper troposphere.(ix) In this reaction scheme, what are the three reactions which are considered to destroy ozone.(x) In this reaction scheme, what is the reaction which is considered to produce ozone?(xi) Calculate the net ozone production rate (prod - loss) (ppbv/day) at the surface.(xii) Calculate the net ozone production rate (ppbv/day) in the upper troposphere.

10. How might global warming affect the oxidizing capacity of the atmosphere (ie. levels of ozoneor OH)? Again specify a reaction if possible.

13. This question involves estimating the number of molecules of ozone produced per CO oxidation.Assume every CO reacts with OH to produce HO2.

CO +OH(+O2)→ CO2 +HO2 k2 = 2.4× 10−13 cm3/molec− sec

The HO2 that is produced can react then with either NO or O3:

HO2 +O3 → OH + 2O2 k2 = 1.6× 10−15 cm3/molec− secHO2 +NO → OH +NO2 k3 = 9.3× 10−12 cm3/molec− sec[M ] = 2× 1019molec/cm3

O3 : 50ppbv

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Assume that every NO2 produced in the second reaction subsequently photolyzes to produce O,which then reacts with O2 to produce O3.

(i) Write down the net rate of ozone production (i.e. production and destruction) associated withthese reactions.

(i) Assume the O3 mixing ratio is 50 ppbv. What is the mixing ratio of NO (in pptv) at which thenet number of ozone molecules produced per CO oxidized is zero?

(ii) Assume an average NO mixing ratio in the troposphere of 100 pptv. How many molecules ofozone are produced per each CO oxidized?

(iii) Assume the mixing ratio of CO in the atmosphere is 80 ppbv, the NO mixing ratio is 10 pptv,and the OH mixing ratio is 1 pptv. what is the net impact in ppbv/day of CO oxidation on the rateof change of ozone?

(iv) The current direct emission of CO into the atmosphere is 4 × 1013 moles/year. Assuming anaverage NO mixing ratio in the troposphere of 100 pptv, how many moles of ozone are producedeach year by CO oxidation?

14. Suppose that there was no NOx in the troposphere so that there was no way to produce ozone.(i) What would then be the only source of ozone to the troposphere?(ii) How would this impact the production of HOx in the troposphere?(iii) How would this impact the chemical composition of the troposphere? Give two examples.

15. Assume the following reactions:1. OH +O3 → HO2 +O2

2. HO2 +O3 → OH + 2O2

3. HO2 +NO → OH +NO2

4. NO2 + hν → NO +OBy imposing steady state conditions on various species, show that the net rate of Ox production byHOx can be written,d[Ox]/dt = - 2 k2 [HO2] [O3]

Oxidizing Power of the Troposphere: Is Ox production Hydrocarbon or NOx limited? (T4)

18. The average emission of NOx over the continental United States is 2 × 1011 molecules cm−2

s−1. Assume that all of this NOx is oxidized and rains out over the United States. The rate of HOx

production PHOx is 4× 106 molecules cm−3 s−1.The only two sinks of HOx are:HO2 +HO2 → H2O2 k1 = 3.0× 10−12 cm3/molec− secNO2 +OH +M → HNO3 +M k2 = 1.0× 10−11 cm3/molec− sec

The [M] dependence has already been included in k2 (i.e. do not need [M].)Model the United States as a well mixed box with a depth of 10 km. i.e. treat all quantities asindependent of height.(i) What is the rate of HOx destruction via reaction (2)?(ii) What is the rate of HOx destruction via reaction (1)?(iii) Would you expect ozone production over the United States to be limited by the availability ofNOx or hydrocarbons? Explain.(iv) Would you expect the mean OH concentration to increase or decrease in response to increasedemissions of NOx? Explain.

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19. (From Chapter 12 Introduction to Atmospheric Chemistry, by Daniel Jacob.) Model the lowertroposphere over the eastern United States as a well-mixed box of height 2 km extending 1000 km inthe east-west direction. The box is ventilated by a constant wind from the west with a speed of 2 ms−1. The mean NOx emission flux in the eastern United States is 2×1011 molecules cm−2 s−1, constantthroughout the year. Let P(HOx) represent the production rate of HOx in the region. As seen inthis chapter, we can diagnose whether O3 production in the region is NOx - or hydrocarbon-limitedby determining which one of the two sinks for HOx, (1) or (2), is dominant:

HO2 +HO2 → H2O2 +O2 (1)

NO2 +OH +M → HNO3 +M (2)

We present here a simple approach for making this diagnosis. It is convenient to assume that thebox has some width w. Refer to the height of the box (2 km) as H, and the length (1000 km) as L.Your answers should be independent of w.The total volume is then V = w ×H × L.Define F (NOx) as the flux of NOx at the bottom of the box (molec/cm2).Define L(NOx) as the loss rate of NOx (in molec/sec · cm2) in the box due to the formation of nitricacid.Define LT (NOx) as the total number of NOx molecules leaving the box by transport per second.Note that it has units of molec/sec, different from L(NOx).

(i) Express LT (NOx) in terms of the dimensions of the box, the horizontal wind speed w, and theNOx concentration.(ii) Assuming that the NOx in the box is in steady state (ie. total flux of NOx into the box per second= number of NOx molecules chemically destroyed in the box per second + number NOx transportedout of the box per second), find the concentration of NOx in the box. Assume that the NOx emittedinto the eastern United States has a lifetime of 12 hours against oxidation to HNO3 by reaction(2). Assume reaction (2) to be the only sink for NOx (a fair approximation during summer). Alsoassume that the NOx concentration of the air entering the box is zero. When you write down theconservation equation, make sure that all the terms are dimensionally consistent.(iii) Calculate the fraction of emitted NOx that is oxidized within the region (vs. ventilated out ofthe region). You should find that most of the NOx emitted in the eastern United States is oxidizedwithin the region.

20. A photochemical model calculation indicates a 24-hour average HOx production rate P(HOx) =4× 106 molecules cm −3 s−1 over the eastern United States in July.(i) Compare this source of HOx to the source of NOx.(ii) Use the criteria given above to conclude as to whether O3 production over the eastern UnitedStates in July is NOx - or hydrocarbon-limited. You may assume that the only two sinks of HOx arereactions (1) and (2) given above.

Oxidizing Power of the Troposphere: CO (T5)

1. (i) CO oxidation can produce O3 in the troposphere. Write down the sequence of reactions bywhich this occurs.(ii) Give a reason as to why this mechanism for O3 production is not very important in the strato-sphere.

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2. The two principal sources of CO to the atmosphere are oxidation of CH4 and combustion.Mean rate constants for oxidation of CH4 and CO by OH in the troposphere are k1 = 2.5 ×10−15cm3molecule−1s−1 and k2 = 1.5 × 10−13cm3molecule−1s−1. Observations indicate mean COconcentrations of 80 ppbv in the northern hemisphere and 50 ppbv in the southern hemisphere, anda globally uniform CH4 mixing ratio of 1700 ppbv. Calculate the fraction of the CO source in eachhemisphere contributed by the oxidation of CH4. You can assume that CO is in steady state withineach hemisphere, and that transport of CO between hemispheres is not important.

3. (i) One of the defining characteristics of the troposphere, as opposed to the stratosphere, is thatOH is more likely to react with CO than O3. Suppose that the O3 mixing ratio was 50 ppbv (atypical tropospheric value). What is the CO mixing ratio at which OH will react with CO and O3

with equal probability?T = 220 KPressure = 220 hPa[M] = 6.6× 1018molec/cm3

O3 = 50 ppbvOH + CO(+O2)→ HO2 + CO2 k1 = 1.7× 10−13

OH +O3 → HO2 +O2 k2 = 2.2× 10−14

(ii) Given the usual range of tropospheric CO mixing ratios, would you expect OH to react morefrequently with CO or O3?

4. (i) What are two sources of methane to the troposphere?(ii) CO concentrations tend to be higher in the Northern Hemisphere than the southern Hemisphere.Give a reason for this.(iii) CO has a seasonal cycle in the Arctic in which it peaks around March and has a minimumaround September. Give an explanation for this cycle in terms of the sources and sinks of CO.

5. (i) Show how the mixing ratios of O3 (ozone) and CO (carbon monoxide) might typically varywith height between 0 and 20 km. Note the tropopause in both plots.(ii) Changes in the O3/CO ratio in going from the troposphere to the stratosphere have a big impacton how HOx affects the ozone budget. Discuss briefly.

6. What are two source of carbon monoxide (CO)?

7. (i) Show how the mixing ratios of O3 (ozone) and CO (carbon monoxide) might typically varywith height between 0 and 20 km. Note the tropopause in both plots.(ii) Changes in the O3/CO ratio in going from the troposphere to the stratosphere have a big impacton how HOx affects the ozone budget. Discuss briefly.

8. In the troposphere CO and O3 tend to be positively correlated in the summer, negatively correlatedin the winter. Explain.

9. (i) In the troposphere, CO concentrations typically build up over the winter, peak in spring anddecrease over the summer. With respect to the sources and sinks of CO, how would you explain thisseasonal cycle?(ii) How does the concentration of CO typically depend on latitude. Explain.

10. Plot how you would expect CO to vary over the course of a year at a mid-latitude location.Explain the increases and decreases.

11. Write down the sequence of reactions involved in the production of O3 by CO oxidation in thetroposphere.

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12. Simultaneous surface based measurements of CO and O3 from Sable island show that CO andO3 are positively correlated in the summer but negatively correlated in the winter. Explain.

Oxidizing Power of the Troposphere: NOx Budget (T6)

13. What is an important natural source of NOx to the troposphere?

14. (i) Model the lower atmosphere over the United States as a well-mixed box extending horizontally5000 km in the west-east direction. There is a constant westerly wind blowing air through the box atU = 10 m/sec. What is the residence time of an air parcel in the box against removal by transport(in days)?Assume the mean concentration of OH in the box is [OH] = 1.2× 106 molecules/cm3. Assume thefollowing reactions, and that NOx can be partitioned using family style approximations. (RememberNOx = NO + NO2.)NO2 +OH → HNO3 k1 = 1.0× 10−11 cm3/molec− secNO +O3 → NO2 +O2 k2 = 9.2× 10−15 cm3/molec− secNO2 + hν → NO +O JNO2 = 0.01 sec−1

O3 : 50ppbv[M ] = 2× 1019molec/cm3

(ii) Solve for the NO/NO2 ratio.(iii) What is the lifetime of an NOx (= NO + NO2) molecule in the box against conversion to HNO3

(in days)?(iv) What fraction of the NOx emitted into the box from the surface will be removed by transport?

Chapter 12: Ozone Air Pollution (X12)

2. (i) Define ozone production efficiency ε (in both words and the chemical definition).(ii) Plot how it depends on the NOx concentration.(iii) Suppose the NOx emissions from a city were to double. Is this likely to double the productionof ozone in that city? Explain.

3. (i) Show a contour plot of how ozone concentrations typically depend on emissions of NOx (thex axis) and emissions of hydrocarbons (the y axis).(ii) In the diagram, show the boundary between the NOx limited and hydrocarbon-limited regimes,and label the two regimes.(iii) In recent years, there has been an increased appreciation of the role of isoprene (a naturallyemitted hydrocarbon) on ozone production in rural areas. How would the presence of isoprene changethe sensitivity of ozone production to NOx emissions. Would it tend to push ozone production intothe NOx or hydrocarbon limited regime? Explain.

5. High ozone episodes in cities tend to occur in summer. Why?

Chapter 13: Acid Rain (X13)

1. In general, would you expect an NOx molecule to travel further before coming back to the surfaceas acid rain in the summer or winter? Explain.

2. The SO2 and NOx emissions of a power plant are making the rain in the area surrounding it moreacidic. Will the affected region be larger in the summer than the winter, or vice versa?

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3. (Problem 13.4 of Jacob) The southern San Joaquin Valley of California experiences extendedstagnation episodes in winter due to strong and persistent subsidence inversions. These stagnationepisodes are often accompanied by thick valley fogs. We use here a box model to describe the valleyair during such a foggy stagnation episode. The top of the box is defined as the base of the inversion,400 m above the valley floor. We assume no ventilation out of the box. The temperature of the boxis 273 K.(i) The major sources of pollution in the valley are steam generators for oil recovery, emitting SO2

with a mean flux E = 4×102 moles/km2 day−1. This SO2 is removed from the valley air by depositionto the surface (first order rate constant kd = 0.5 day−1) and by oxidation to H2SO4 (first order rateconstant k0 = 1 day−1). Calculate the steady state SO2 mixing ratio in the valley in units of ppbv.You can assume the SO2 emission is everywhere instantly well mixed up to the base of the inversionlayer (400 m). Compare to the U.S. air quality standards of 140 ppbv for 1-day exposure and 30ppbv for 1-year exposure. Remember that at STP conditions, which you can assume here, 1 mole ofair will occupy 22.4 litres, and 1 liter is 1000 cm3.

(i) AnswerThere are lots of different ways to do the question. Here is one:First convert the emission to an effective production equally spread from the ground to H (= 0.4

km)P = E/H = 1000 moles SO2/km3/dayAt this point, the best thing to do is probably convert this P to moles SO2/moles air/day.The number of moles of air in 1 km3 can be obtained by1 km3 = 1.0E+15 cm3 = 1.0E+12 liters1.0E+12 liters of air contains 4.46E+10 moles of air (dividing by 22.4).So P = 2.2E-08 moles SO2/moles air/day = 22 ppbv SO2/dayDefine CSO2 as the SO2 mixing ratioAt steady state,dCSO2/dt = P - kd*CSO2 - k0*CSO2 = 0Solving for CSO2:CSO2 = P/(kd + k0) = (22 ppbv SO2/day)/(1.5 1/day) = 14.7 ppbv SO2This is lower than the U.S. air quality standard.

(ii) Sulfuric acid produced from SO2 oxidation in the valley air is incorporated immediately into thefog droplets. These fog droplets are then removed from the valley air by deposition with a first-orderrate constant k′d = 2 day−1. The liquid water content of the fog is 1 × 10−4 l water per m3 of air.Calculate the steady-state fog water pH if H2SO4 is the only substance dissolved in the fog droplets.(Hint pH = -log [H+], where [H+] is in moles per liter).

(ii) AnswerLet CH2SO4 by the H2SO4 mixing ratio.dCH2SO4/dt = k0*CSO2 - kd’*CH2SO4 = 0CH2SO4 = (k0/kd’)*CSO2 = (1/2)*14.7 ppbv = 7.4 ppbvSuppose you have 1 mole of air, or 22.4 litres.In 1 m3 of air, there is 1E-04 liters of water.1 m3 = 1E+06 cm3 = 1000 liters = 44.6 molesSo 1 mole of air will have 1E-04/(44.6) = 2.2E-06 liters of waterSo we have 7.4E-09 moles of H2SO4 in 2.2E-06 liters of water.Each H2SO4 releases 2 H+ (strong acid).Therefore [H+] = 2*7.4E-09 moles/2.2E-06 liter = 0.0067 moles/l

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This gives pH = 2.2(iii) In fact the valley also contains large sources of ammonia from livestock and fertilized agriculture.The NH3 emission flux is estimated to be 5.6×102 moles/km2 day−1. Is it enough to totally neutralizethe H2SO4 produced from SO2 emissions?

(iii) AnswerThis does not involve a complex calculation.Note that 2/3 of the emitted SO2 is oxidized to H2SO4.But each H2SO4 produces 2 H+.So the effective production of H+ is 2*(2/3)*400 moles/km2/day = 533 moles/km2/dayEach emitted NH3 can neutralize one H+.Since 560 is larger than 533, the emitted NH3 can neutralize the H2SO4.

4. Calculate the fraction of aqueous phase ammonia (ie. NH3 ·H2O + NH+4 ) to gaseous ammonia

(NH3) at a pH of 5.6 at a temperature of 273 K in a cloud of liquid water content 4 × 10−6 cm3

water per cm3 air. Do the same for the cloud droplets with a pH of 3. You will first have to derivean expression for the pH dependent effective Henry’s Law constant H∗ for total dissolved ammonia.

5. What are two chemical species whose presence can help offset increased acidity in rainwaterassociated with enhanced atmospheric concentrations of NOx and SO2. In each case, show therelevant reactions by which the concentration of [H+] in cloud or rainwater is reduced.

6. The gas phase mixing ratio of SO2 in an air parcel is 2 ppbv. After a cloud forms, the mixingratio of SO2 decreases as some of the SO2 enters the cloud droplets. Inside the cloud droplet, andequilibrium between SO2 ·H2O, HSO−3 , and SO2−

3 , is quickly established. The solubility of SO2 inwater is determined by the following:

SO2 +H2O ⇀↽ SO2 ·H2O HSO2 = 1.24M

atm

SO2 ·H2O ⇀↽ H+ +HSO−3 Ks1 = 1.29× 10−2M

HSO−3 ⇀↽ H+ + SO2−3 Ks2 = 6.014× 10−8M

Define:[S(IV)] = [SO2 ·H2O] + [HSO−3 ] + [SO2−

3 ]Then Henry’s Law can be expressed:

[S(IV )] = H∗PSO2 ,

where,

H∗ = H[1 +Ks1

[H+]+Ks1Ks2

[H+]2]

and

pH = −log[H+].

Also note that the ideal gas law can be expressed

PV = nRT,

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where P is the pressure in atm, V is the volume in liters, n is the number of moles, the ideal gasconstant R = 0.082 atm

M ·K .(i) Find the gas phase mixing ratio of SO2 in the cloud. Assume the pressure is 500 hPa, or 0.5 atm,that the temperature is 250 K, the cloud liquid water fraction = 1× 10−7, and the pH of the clouddroplets is 2.(ii) Assume instead that the pH of the cloud droplets is 5. What is the gas phase mixing ratio ofSO2?

7. The rate of aqueous phase S(IV) oxidation by hydrogen peroxide is given by

−d[S(IV )]

dt=k[H+][H2O2][S(IV )]α1

1 +K[H+],

where,

k = 7.45× 107M sec−1

K = 13 M−1

α1 =[HSO−3 ]

[S(IV )].

The solubility of S(IV) in water is determined in part by the following reactions.

SO2 +H2O ⇀↽ SO2 ·H2O HSO2 = 1.24M

atm

SO2 ·H2O ⇀↽ H+ +HSO−3 Ks1 = 1.29× 10−2M

HSO−3 ⇀↽ H+ + SO2−3 Ks2 = 6.014× 10−8M

Also,

pH = −log[H+]

H2O2 +H2O ⇀↽ H2O2 ·H2O HH2O2 = 7.1× 105 M

atm

Assume that a cloud of liquid water content L = 10−7, contains 20 ppbv of gas phase SO2, and 6ppbv of total H2O2. The cloud has a pH of 5. By total is meant the sum of the actual gas phasemixing ratio of H2O2 plus what the contribution of aqueous phase H2O2 to the gas phase wouldbe after conversion from molarity to mixing ratio. The ideal gas constant is R = 0.082 atm

M ·K . Thepressure is 1 atm and the temperature 298 K.(a) Calculate [H2O2], the molarity of hydrogen peroxide in the liquid phase.

(b) Calculate [S(IV)] and α1.

(c) Calculate the lifetime of an aqueous phase hydrogen peroxide molecule with respect to the lossby oxidation of S(IV). Convert this to a lifetime for total H2O2. Are the losses of H2O2 via gas phasephotolysis and attack by OH likely to be important processes within the cloud?

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8. Give one of the chemical reaction(s), or series of chemical reactions, by which dust, or an ”agri-cultural emission”, increases the pH of rain.

9. The gas phase concentration of ammonia (NH3) at the ground is 5 ppbv. Calculate the pHof a water droplet near the ground if ammonia is the only soluble gas phase species present. Thetemperature is 298 K.

NH3(g) +H2O → NH3 ·H2O HNH3 = 62M

atm

NH3 ·H2O → NH+4 +OH− Ka = 1.71× 10−5 M

H2O → H+ +OH− Kw = 1.0× 10−14 M2

pH = −log[H+]

10. The presence of ammonia (NH3) in a cloud can increase the rate of aqueous phase oxidation ofS(IV) to S(VI). Explain.

Glossary for Atmospheric Chemistry

Nitrogen:Nitrogen N2

Nitric Oxide NONitrogen Dioxide NO2

Nitric Acid HNO3

atomic Nitrogen NNitrous Oxide N2O

Hydrogen:atomic hydrogen Hwater H2OHydroxyl radical OHPeroxy radical HO2

Hydrogen Peroxide H2O2

Chlorine:Chlorine Monoxide ClChlorine Dimer Cl2O2

Chlorine Nitrate ClONO2

Hydrochloric Acid HClCFC’s eg CFCl3, etc.

Methane and its products:Methane CH4

Methyl CH3

Methyl Peroxy CH3O2

Formaldehyde CH2OCarbon Monoxide COCarbon Dioxide CO2

Ethane C2H6

Oxygen:

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Oxygen O2

Atomic Oxygen OExcited Atomic Oxygen O1DOzone O3

Various:Dimethyl Sulphide (CH3)2SSulphuric Acid H2SO4

Sulphur Dioxide SO2

Hydrocarbon methane, ethane, etc.PSC Polar Stratospheric Cloud

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